17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

Q: Take k to be a positive real number. Suppose that u is the solution to the diffusion equation Ut =…

A:

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

A:

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

A:

Q: Find y". y = edx sin Bx y" =

A:

Q: y*dxdy V2 y у?)2 2 3/2 (x² +

A: Here we have to evaluate I=∫01∫0yy2dxdyx2+y232=22

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: 04) Find dy /dx for the following functions: a) y².cotx= [sin(x.y)]-¹ b) y = (lnx + x)tan

A: See the answer below

Q: 2. Differentiate. f(t) = et sin(2t)

A:

Q: | sin x (3cosx)dx 2: VZ 3x dx V1- x4 3:

A: SOLUTION-

Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

A:

Q: 2. Integrate | sin x cos? x dx

A:

Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

A:

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: Find when y = cos(sin 2x). ay dx dy dx

A:

Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

A:

Q: ) dx dy is

A:

Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

A:

Q: find af/ax and ðf/əy +4- 17. f(x, y) = sin² (x – 3y) %3D

A:

Q: Q4) Find for the following functions (choose five only): dx 1. y = 2 +etr-1 2. y = sec x tan x 3. y…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.